Question

The table shows the classification of $100$ families in a locality according to the amount paid against their electricity bill.

Electricity bill (in Rupees)	Number of families
$0-200$	$8$
$200-400$	$12$
$400-600$	$21$
$600-800$	$30$
$800-1000$	$23$
$1000-1200$	$6$

Find the median of the amount paid.

Answer 1

The table below shows the number of families paying electricity bill below each rupee:

Electricity bill (in rupees)	Number of families
Below $200$	$8$
Below $400$	$8+12=20$
Below $600$	$20+21=41$
Below $800$	$41+30=71$
Below $1000$	$71+23=94$
Below $1200$	$94+6=100$

Now we have,

$x$	$200$	$400$	$600$	$800$	$1000$	$1200$
$y$	$8$	$20$	$41$	$71$	$94$	$100$

Now, median is the number $x$ which gives $y=\frac{100}{2}=50$, which lies between $y=41$ and $y=71$.
Thus, using proportionally assumption, we have
$\frac{x-600}{800-600}=\frac{50-41}{71-41}$
$\Rightarrow \frac{x-600}{200}=\frac{9}{30}$
$\Rightarrow x-600=\frac{9}{30}\times 200=60$
$\Rightarrow x=660$
Thus, the median of the amount paid is $660$.